Multiple pulse laser-induced damage phenomena in silicates

Multiple pulse laser-induced damage phenomena in silicates

Dimitrios Kitriotis and Larry D. Merkle

Multiple pulse laser-induced bulk damage has been studied in fused silica and borosilicate glass. The fluence

dependence and pulse repetition frequency dependence of the damage make it clear that laser irradiation

promotes damage on subsequent pulses, and the evidence favors attribution of the effect to transient entities

such as point defects rather than larger imperfections such as inclusions. However, the influence of

preirradiation defects on damage thresholds is small, and a luminescence experiment places low limits on the

possible concentration of conduction band electrons prior to damage. The constraints these results place on

possible mechanisms of multiple damage are briefly discussed.

1. Introduction

In recent years the phenomenon of multiple pulselaser-induced damage to the bulk of a transparentsolid has received growing attention, but the mecha-nisms involved remain very uncertain.1-7 In this phe-nomenon a material is observed to suffer damage afterexposure to a train of laser pulses, each of which hasirradiance too low to cause damage in a single pulse.There is disagreement as to whether the pulses preced-ing observable damage induce property changes in thematerial which promote subsequent damage,3 -6 orwhether the eventual damage simply represents a sta-tistical effect.7'8 In the latter case damage after manypulses is believed to occur due to either the incidence ofan anomalously high-irradiance pulse or the presenceof a nonzero probability of damage on any pulse even atirradiances significantly below the usually recognizedsingle pulse damage threshold. In some materials thenumber of pulses required to induce catastrophic dam-age at a given irradiance depends on the pulse repeti-tion frequency, making it clear that at least in thesecases repeated irradiation does change the propertiesof the sample, and does so in a transient way.5'9 "10

Identification of a mechanism by which repeatedlaser pulses may reduce a material's resistance to laserdamage has proved difficult for several reasons. Inmost cases the average power absorbed and the focalvolumes irradiated are far too small for cumulative

When this work was done both authors were with University of

Arkansas, Physics Department, Fayetteville, Arkansas 72701; D.

Kitriotis is now at 108 Leon Iasonidi, 60100 Katerini, Greece.

Received 30 June 1988.0003-6935/89/050949-10$02.00/0.

© 1989 Optical Society of America.

heating to explain this phenomenon. In certain casesthe growth of microscopic defects has been observed toprecede catastrophic damage,3 611 but in other casesmaterial changes prior to damage have not been de-tectable.4 5 Preexisting defects, even in such low con-centrations that identification is difficult, can dramat-ically affect the damage properties of a solid, making itdifficult to separate intrinsic and extrinsic damagemechanisms.61 213 In addition, there is no agreementregarding even the mechanism of intrinsic single pulsedamage.' 4 15

In this paper we present the results of several experi-mental tests undertaken to investigate the multiplepulse damage mechanism in BK-7 borosilicate glass,fused silica, and a high quality sample of crystallinequartz. These tests include basic multiple pulse dam-age measurements at 1064 and 532 nm, investigationsof the influence on the damage data of certain preexist-ing point defects, and a search for recombination lumi-nescence on the pulses prior to catastrophic damage.

The remainder of the paper is organized as follows.Experimental apparatus and procedure are summa-rized in Sec. II, the basic damage data are presented inSec. III, and the results of the luminescence search arereported in Sec. IV. A recently reported test of theaccumulative vs statistical origin of multiple pulsedamage8 is applied to the data in Sec. V. The resultsare discussed and compared with possible mechanismsfor multiple pulse damage in Sec. VI.

I. Experiments

The apparatus used for the basic damage experi-ments has been described elsewhere, so that only abrief description is given here.13 Laser irradiation wascarried out by the fundamental and frequency doubledoutputs of a Quanta Ray DCR-1 Q-switched Nd:YAGlaser operated at ten pulses per second. Its annularbeam shape was converted to an approximately Gauss-

1 March 1989 / Vol. 28, No. 5 / APPLIED OPTICS 949

ian profile by a spatial filter. The beam was focusedinto the bulk of the sample to a spot of several micronradius (defined by the radius at which the fluence is e-2times its on-axis value). Due to the multiple axialmode operation of this laser, the pulse profiles werecomplex and varied from pulse to pulse, as describedby other DCR-1 users.6 Using a silicon PIN photodi-ode and a Tektronix 7904 oscilloscope, giving an over-all time resolution of -2 ns, the waveform at 1064 nmappeared to be a pulse of 16-ns full width at half-maximum with superimposed random peaks of ampli-tude -3% of the pulse height. Using the same detec-tion system at 532 nm the 10-ns pulse containedrandom peaks observed to be 20% of the pulse height.Since this is a much greater modulation than would beexpected from squaring the observed 1064-nm wave-forms, it must be concluded that the amplitude of thestructure on the laser pulse is much greater than ourphotodiode could resolve. Indeed, this is to be expect-ed since the bandwidth of the laser, 10 GHz, greatlyexceeds that of the detection system. Due to the inde-terminacy of the waveforms all data are presented interms of on-axis fluence rather than peak irradiance.

A series of silicon photodiodes, an analog-to-digitalconverter, and an LSI-11 computer were used to countlaser pulses and monitor the incident and transmittedpulse energies. The truncation of the transmittedpulse was used as the primary indicator of catastrophicdamage, which event was also accompanied by a flashof light, increased light scatter from a coaxial He-Nelaser, and the production of cracks and bubblelikefeatures in the laser beam focal volume.

For certain experiments BK-7 glass samples were xirradiated prior to the laser damage measurements.This was carried out by placing the sample 10 cmfrom the exit port of a Philips Norelco x-ray diffractioninstrument providing unfiltered Mo radiation. The x-ray tube was operated at 50 kV and 15 mA, and expo-sure times of 3, 6, and 11 h were used.

Searches for luminescence prior to catastrophicdamage were made using a Tracor Northern TN-6500optical spectrum analyzer equipped with a photodiodearray and a microchannel plate intensifier. With a lowdispersion spectrograph this permitted sensitive de-tection of light over a broad spectral range followingeach laser pulse. The collection optics and entranceslit were chosen such that the experiments monitored asegment of the laser beam path -0.5 mm long. Peri-odic adjustments of the alignment were made usinglight scattered from damaged sites to assure that theregion monitored included the laser focal plane. Thesensitivity of the detection system was determined at633 nm using a He-Ne laser and attenuators. Fromthis and the manufacturer's sensitivity curve it is esti-mated that in the spectral region of greatest interest,400-450 nm, the system records about one count foreach ten photons passing the spectrograph entranceslit. For the collection optics employed and assumingany luminescence to be isotropic, this corresponds toabout one count per 3000 emitted photons.

The luminescence searches were carried out at ap-proximately liquid nitrogen temperature using a sim-ple liquid nitrogen optical cryostat. Its vacuum sys-tem included a nitrogen cold trap to avoid depositionof pump oil on the sample. The windows of the cryo-stat were flat to within 1/10 wave to minimize distor-tion of the irradiating beam.

The samples studied were as follows. Schott BK-7borosilicate glass and Corning 7940 fused silica sam-ples were cut from commercially obtained researchgrade windows. For comparison with the high-OH7940 fused silica, a sample of a new grade of fused silicawith only a few parts per million of OH but with purityotherwise similar to 7940 was provided by the CorningGlass Works. The luminescence studies employed anultrahigh purity sample of crystalline quartz grown bythe Electronic Materials Section of the Rome Air De-velopment Center, Hanscom Air Force Base. Onesample of the glass ceramic Cer-Vit C-101 was alsostudied, which was donated by Litton Guidance andControl Systems.

Ill. Damage Data

Representative sets of damage data are presented inFigs. 1 and 2. In each figure each point represents theresult of laser irradiation of a single site in the sample.The abscissa gives the on-axis fluence per pulse towhich the site is exposed, and the ordinate gives thenumber of pulses required to produce damage. In Fig.1 the fluence values for irradiation of BK-7 glass at 532nm at each focal spot size are normalized by the on-axisfluence required to cause damage in a single pulse atthat spot size. The figure compares the multiple pulsedamage curves for three different focal spot radii,showing that damage occurs within a given number ofpulses at a smaller fraction of the single pulse damagethreshold as the spot radius increases. This trend canalso be seen in comparisons of other experiments sum-marized in Tables I and II. In these tables the behav-ior of each set of damage experiments is characterizedby the threshold fluence required for damage to occurwithin 1, 1000, and in some cases 150 or 300 pulses.The threshold for damage within N pulses, FN, is de-fined as the average of the lowest fluence at whichdamage ever occurs within N pulses and the highestfluence at which damage ever fails to occur within Npulses. Note that not only does the ratio F 000 /F, varywith focal spot radius, but F decreases rather marked-ly as the focal radius increases. This is consistent withthe behavior often observed in laser-induced damagestudies and has been attributed to the presence ofcoarsely spaced defects which lower the material's re-sistance to damage.16"17 The spot radius dependenceobserved in this study is probably due to- a similareffect.

Self-focusing may give rise to a qualitatively similarspot size dependence. However, due to the effect ofplasma defocusing at intensities near damaging levels,self-focusing is not expected to be significant for spotradii smaller than a critical limit.17-9 This limit de-pends on the irradiance at which damage occurs, and

950 APPLIED OPTICS / Vol. 28, No. 5 / 1 March 1989

103u)LU

2IL 100

LU

D: 10z

10109

Q5

FLUENCE/F 1

1.0

Fig. 1. Laser-induced damage data for BK-7 borosilicate glass

irradiated at 532 nm. For the experiments denoted by crosses thespot radius is 6.0 pim, whereas for the open squares it is 8.0 um and forthe filled circles it-is 14.0 pm. The focal spot radius is defined as the

distance from the beam axis at which the fluence is down by the

factor e-2 . The pulse repetition frequency for all cases is 10 Hz.The single pulse damage thresholds, F1 , are given in Table I.

due to the complex waveform of the laser employed inthis study this is difficult to evaluate. However, com-parison with single-mode laser damage data4'5 indi-cates that self-focusing is not likely in the presentstudy.

The data presented in Fig. 2 show that the multiplepulse damage behavior of Corning 7940 fused silicaunder 532-nm irradiation depends on the repetitionfrequency of the train of laser pulses. The pulse repe-tition frequency at the sample was varied by interrupt-ing the beam while leaving the repetition frequency ofthe laser constant, so as to avoid changes in the beamshape. The fluence at which the number of pulsesneeded for damage tends toward infinity increases asthe pulse repetition frequency is reduced. This be-havior is consistent with earlier reports and indicatesthat the laser pulses preceding observable damagemust induce damage-promoting changes in the materi-al, at least some of which are transient. 5'9 However,similar comparisons of data for Corning 7940 irradiat-ed at 1064 nm and for BK-7 irradiated at either wave-length show smaller fractional changes with pulse rep-etition frequency, perhaps negligible in view of thescatter in the data. This suggests that, if damage-promoting changes are induced in these cases, theymust be long-lived compared to the 0.1-4-s time inter-vals between pulses.

The observed morphologies of the damage sites inthis work, examples of which are shown in Fig. 3,exhibit a shape consistent with the shape of the high-fluence portion of the beam path, unlike the behaviorexpected for damage at inclusions, in which the shapesand positions of damage sites should reflect those ofthe inclusions. This, in combination with the report-ed lack of change in scattered light levels prior to

LdL U0 532 nm

_j XD El

cK200 x

050 100

FLUENCE (J/cm2)

Fig. 2. Laser-induced damage data for Corning 7940 fused silicairradiated at 532 nm. The crosses represent data taken at a pulserepetition frequency of 10 Hz, whereas for the open squares it is 1 Hzand for the filled circles it is 1/3 Hz. The focal spot radius in all cases

is 12.0 pm.

multiple pulse damage in fused silica,4 5 makes it un-likely that the growth of absorbing inclusions is re-sponsible for the damage behavior. However, there issome variability in damage morphology, as exempli-fied by the presence of a narrow spindle of damage atthe initiation end of the damaged site in Fig. 3(b) butnot in Fig. 3(a). In addition, the ends of the damagedregions at which damage originates are found to lie inthe same plane within -25 Am. This small but non-zero variation indicates that damage initiation is de-termined primarily by the high fluence at the focalplane, but that some inhomogeneity may be present.Thus, impurities or defects may well play a role in thedamage process.

Tables I and II show a marked wavelength depen-dence in the damage thresholds of each material stud-ied. For example, fused silica thresholds at 532 nm areabout one-twentieth of the 1064-nm thresholds forcomparable focal spot radii. A similar trend has beenobserved in this laboratory for crystalline quartz.13

However, damage studies of both crystalline quartzand fused silica using a YAG laser of similar pulseduration and focal spot radius but with a smooth wave-form exhibited a far smaller difference in damagefluences between 1064 and 532 nm.4'5 Based on thediscussion of Sec. II, it is very probable that the 1064-nm waveform used in the present study contains in-tense peaks of short duration, and the amplification ofthose peaks by frequency doubling makes them evenmore important at 532 nm. Therefore the wavelengthdependence of the peak irradiation cannot be assumedto match that of the fluence. For this reason thestrong wavelength dependence of the observed damagethresholds of SiO2 must be regarded as due primarilyto the laser waveforms rather than material properties.

Table I shows that the wavelength dependence ofthe single and multiple pulse thresholds in BK-7 andthe glass ceramic is even stronger than in SiO2 . This is


- E K-

-*

- .

_ 9.

- . @.4

l I ,,,i

BK-7

,32 m -

_

.o

R_

.- t

probably due to the much smaller band gaps of thesematerials. Strong interband absorption begins at-3.8 eV in BK-7 and at -3.2 eV in Cer-Vit C-101, sothat two-photon absorption should occur at 532 nm inboth. The particularly small band gap in the glassceramic also helps to explain the fact that its damagethresholds at both wavelengths are lower than those ofBK-7.

Some of the damage experiments were performed onBK-7 samples previously irradiated by x rays to pro-duce point defects. This is of interest because it hasbeen reported that irradiation of BK-7 by 532-nm laserpulses at irradiances significantly below the levelsneeded to produce catastrophic damage generatespoint defects which absorb visible light.20 It is thus

possible that defects generated on one pulse promotedamage on a subsequent pulse, thus playing a role inthe multiple pulse damage phenomenon. Figure 4shows the x-ray-induced absorbance from 390 to 610nm for the three x-irradiation times used in this study.The spectra are not identical to that reported by Whiteet al.,20 but the same primary features are present: thewing of a strong ultraviolet absorption and evidence ofa weaker absorption band in the visible. Absorptionmeasurements were also made along light paths per-pendicular to the x-ray beam path at several depths,permitting determination of the 532-nm on-axis laserfluence in the focal plane to an accuracy of a fewpercent. These measurements also yield an approxi-mate 532-nm absorption coefficient at the focal plane

Table I. Summary of Damage Data on Boroslllcate Glass BK-7 and Glass Ceramic Cer-Vit C-1018

Pulse repetition Focal spotWavelength frequency radius F1 F 1000Sample (nm) (Hz) (Am) (J/cm 2 ) (J/cm 2 )

BK-7 1064 10 7.5 3000 1400(F300 = 1500)

BK-7 1064 1/4 7.5 3000 (F3 00 = 1450)BK-7 1064 10 7.5 2900 1450

(x irradiated 11 h)BK-7 532 10 6.0 84 52BK-7 532 10 8.0 54 30BK-7 532 10 14.0 42 20BK-7 532 10 14.5 40 20BK-7 532 10 12.5 42 21

(F3lo = 22)BK-7 532 1 12.5 42 (F300 = 25)BK-7 532 10 12.5 39 19

(x irradiated 3 h)BK-7 532 10 12.5 40 23

(x irradiated 6 h)C-101 1064 10 7.5 800 520

(Glass ceramic)C-101 532 10 6.0 15 8

(Glass ceramic)

a The focal spot radius is that radius at which the fluence is down by e 2from its on-axis value. The threshold fluences for damage due to asingle pulse and due to 1000 pulses, F and F1000 , respectively, are defined in the text. The threshold fluence for damage in 300 pulses, F 300, isgiven in cases where data do not extend to 1000 pulses or for comparison with such cases.

Table II. Summary of Damage Data on Corning 7940 (1000-ppm OH) and Water-Free (a few ppm OH) Fused Silica; the Parameters Have the SameMeanings as In Table I

Pulse repetition Focal spotWavelength frequency radius F1 F10oo

Sample (nm) (Hz) (Am) (J/cm 2 ) (J/cm 2 )

7940 1064 10 7.5 3800 2050Water free 1064 10 7.5 3600 1750

7940 1064 10 12.5 1500 760(F300 = 800)

7940 1064 1/3 12.5 1500 (F300= 860)7940 532 10 5.5 455 175

Water free 532 10 5.5 330a 1907940 532 10 6.0 245 (F300 = 145)7940 532 10 12.0 110 55

(F150 = 60)7940 532 1 12.0 110 65

(F15o = 65)7940 532 1/3 12.0 110 (F1 5o = 75)7940 532 10 14.5 110 55

a This low value is strongly affected by the unusually large scatter in the damage data; see Fig. 8.


4-Beam Direction

(a) (b)

Fig. 3. Two typical sites in Corning 7940 fused silica damaged by 532-nm irradiation.

of 1.6 cm-' in the 6-h x-irradiation region. Since theproperties of point defects in BK-7 are not well known,it is not possible to infer a defect concentration fromthis value at present. The induced absorbance wasnegligibly small at 1064 nm. The laser-induced dam-age data comparing irradiated and unirradiated re-gions are presented in Figs. 5 and 6. The data of Fig. 5show no evidence that x-ray-induced point defectsaffect the 1064-nm damage properties of BK-7. Dueto the imprecision of the calculated beam attenuationat 532 nm, the variation of absolute damage thresholdvalues in Fig. 6 is probably within experimental error.The shapes of the 532-nm damage curves give someevidence that the presence of point defects may havean effect on damage at this wavelength, since the curveis steeper for the region x irradiated for 6 h than for the

unirradiated material. However, it is clear that theeffect of the radiation-induced defects on laser damageis small.

A comparison has been made of the damage proper-ties of two grades of fused silica whose major differenceis hydroxyl content. This is of interest because thepresence or absence of OH has a significant effect onthe types of point defect present in fused silica, withlow-OH material having a much higher concentrationof such defects as Si-Si bonds and Si-O-O-Si bonds,whereas in the high-OH material defects such as Si-OH are more common.21 These in turn affect thematerial's response to radiation, including the genera-tion of metastable E' centers and other defects byultraviolet light at energies below the band gap.2223 Ithas been reported that the presence of E' centers in


0.3

X) Ao0 BK-7z 0

< ~~A<Q2 6 HRS A 11 HRS0 A

0o o AA 0

nx A 001Q X AA 00U x AA

13H- iR XA

X nU BK-7X

_ ~~~~xx<

0 1 430 510 590WAVELENGTH (rim)

Fig. 4. Absorption spectra of x-irradiated BK-7. The times referto the number of hours of irradiation.

UN IRRADIATE

i 3- X-IRRADIATED

0 6102co

100

1000 3000FLUENCE (j/CM 2)

Fig. 5. Dependence on x irradiation of 1064-nm laser-induced dam-age in BK-7. The crosses correspond to data on unirradiated mate-rial, the open squares to data on material xirradiated forl11h. Thefocal spot radius is 7.5 m and the pulse repetition frequency is

10 Hz.

fused silica lowers its 532-nm damage threshold, 2 4 sothat it is possible that generation of such defects (per-haps by nonlinear absorption at the high irradiancesassociated with laser damage) contributes to the multi-ple pulse damage mechanism. As shown in Fig. 7, thedamage thresholds in Corning water-free fused silicaare lower than those in Corning 7940, although themagnitude of the difference is small. Since the changeis comparable for single pulse and multiple pulsethresholds, the difference in damage behavior maywell have more to do with the final damage event thanwith the generation of laser-induced defects on previ-ous pulses. The situation is less clear for 532-nmdamage, as seen in Fig. 8. Application of the thresholddefinition given earlier would indicate that the singlepulse threshold is significantly lower in the low-OHsample. However, the figure shows that the great

en

LU

0-JDa 2, 100LU

ED 10z

0 30 * 60FLUENCE (J/cm2 )

Fig. 6. Dependence on x irradiation of 532-nm laser-induced dam-age in BK-7. The crosses correspond to data on unirradiated mate-rial, the open squares to material x irradiated for 3 h and the filledcircles to material x irradiated for 6 h. The focal spot radius is 12.5

Am and the pulse repetition frequency is 10 Hz.

Ld

-J11D

rLL0a

LUJco

2~

10 3

2

101

1001500 3500FLUENCE (J/cm2)

Fig. 7. Laser-induced damage data for two grades of fused silica at1064 nm. The crosses correspond to data on Corning 7940, a materi-al with high OH content, the filled circles to data on a water-freefused silica from Corning, having only a few parts per million OH.The focal spot radius is 7.5 Am and the pulse repetition frequency is

10 Hz.

majority of the water-free fused silica data overlap the7940 data very well. Thus, the several damage eventsat lower fluences in the water-free material may simplyindicate inhomogeneity in this sample. Therefore, theevidence that the difference in point defects betweenthe samples affects damage properties must be consid-ered weak.

IV. Luminescence Experiment

The two most prominent models for single pulselaser-induced damage in cases not dominated by inclu-


I . I UNIRRADIATED

Ad VS X-RAY_ f IRRADIATED-

* BK-7

532 nmBhe

t is

w~~~a

_ w&>

I I I I I I I I -FUSED SILICA:.

LOW-OH-AND -V 7940

*] X 1064 nm

a x xe )* XX

-, I, I, I I >

lb0:

I

to )* 7940U)

XX 532 nm

L 10

LU

co X10 0

0~~~~i

100 0 00*&0 200 400

FLUENCE (J/cm2 )

Fig. 8. Laser-induced damage data for two grades of fused silica at532 nm. The crosses correspond to experiments in which damage

was observed in the indicated number of pulses in Corning 7940, the

open squares to experiments in the same material which were termi-nated without damage. The filled circles correspond to experimentsin which damage was observed in the indicated number of pulses in

the Corning water-free sample. The filled triangles correspond toexperiments in the same material which were terminated withoutdamage. The focal spot radius is 5.5 ,um and the pulse-repetition

frequency is 10 Hz.

sion heating are electron avalanche'5 and multiphotoncarrier generation followed by free-carrier absorp-tion,'4 both of which involve the production of a highconcentration of electrons and holes. It is thus possi-ble that multiple pulse damage involves a process bywhich the concentration of electrons and holes in-creases from pulse to pulse by the trapping of chargesgenerated by one of these mechanisms, eventuallyreaching damaging levels. It is therefore of interest toseek evidence of the electron-hole concentration priorto the pulse on which catastrophic damage occurs.

In this context a search has been made for the 450-nm luminescence reported to follow the irradiation ofquartz and fused silica by ionizing radiation.2 5 Thisluminescence is believed to result from the recombina-tion of a transient oxygen vacancy-interstitial Frenkelpair, created by the interaction of an electron andhole.26 Indeed in quartz, where the emission is stron-ger than in fused silica, a lower limit on the probabilityof luminescence per electron-hole pair may be esti-mated so that the luminescence can serve as a monitorof the electron density. The number of oxygen vacan-cies created per unit of absorbed energy in electronirradiation experiments on quartz is -1.3 X 10-2 eV-,and the weak temperature dependence of the lumines-cence below 150 K suggests that the low temperatureluminescence quantum efficiency is near one.2526 Ifthe energy deposited in the electron irradiation experi-ments creates the maximum possible number of elec-

tron-hole pairs, the resulting minimum number ofphotons emitted per electron-hole pair is -0.135.

In the present study the optical spectrum analyzersystem described in Sec. II was used to look for emis-sion from the laser-irradiated sample volume in a spec-tral region -130 nm wide positioned to overlap thisemission band while avoiding the laser wavelength.The experiments were carried out on quartz at liquidnitrogen temperature to achieve a high quantum effi-ciency, using both 1064- and 532-nm laser irradiation.The quartz sample used was an ultrahigh purity mate-rial grown by the Rome Air Development Center ofHanscom Air Force Base, as it has been found that thismaterial exhibits more nearly intrinsic damage behav-ior than other available quartz samples.13 The dam-age properties of quartz at nitrogen temperature havebeen found to differ only modestly from room tem-perature behavior, so that the low temperature testshould be applicable to the present study.27 At thislow temperature the fluorescence lifetime of the 450-nm emission is -1 ms,26 for which reason the photodi-ode array was used with its minimum 5-ms exposuretime. It was found that signal averaging over 100pulses was needed to achieve a satisfactory noise level,so measurements were concentrated in the range offluences for which damage occurred within a few hun-dred to a few thousand pulses.

The experiments showed no luminescence prior tothe onset of catastrophic damage. The difference be-tween the luminescence signal integrated over thespectral region of interest and the background with nolaser has a root mean square value of 34 counts. Thiscorresponds to a detection limit of -7.5 X 105 electron-hole pairs. The corresponding electron density de-pends on the electron distribution in the sample andthus on the excitation process. Using the focal spotradius of the 532-nm laser beam, 5.5 /m, the detectionlimit of the on-axis concentration for electrons createdby one-photon absorption is -2 X 1013 cm-3, whereas itis 5 X 1013 cm- 3 for two-photon, 9 X 1013 cm- 3 forthree-photon, and 1.4 X 1014 cm- 3 for four-photonabsorption. The concentration of free electrons typi-cally regarded as necessary for catastrophic damage is-1018-1020 cm-3. Thus, the null result of the lumines-cence experiment indicates that the density of freeelectrons created by any low-order absorption processprior to damage must be quite small compared with thedensity expected to be created on the damaging pulseitself.

Since catastrophic damage is accompanied by abright flash of light and the luminescence spectra wereaveraged over 100 pulses, the spectra due to the lastfew tens of pulses prior to damage were generally oblit-erated by the flash. Thus, the concentration limitdoes not apply to the last several percent of a typicalmany-pulse damage experiment.

The luminescence experiments were repeated onfused silica, with the same null result. Due to thelower efficiency of vacancy generation and lumines-cence in this material,2526 this result gives less strin-gent concentration limits than in quartz.


J

0

al

C 1

LJ

0

<0

<10

0

N =3 -o~~/-

N=100-2 I = 30 5-40 I~~~~~

0-20 012 2 5-30 13 3 5-40 120-25 30-35 40-45

FLUENCE INTERVAL (J/cm2)

45i-

Fig. 9. Comparison of observed probabilities for damage within agiven number of pulses and predictions based on the assumptionthat predamage pulses do not modify the damage probability. Thefilled circles represent the probability of damage within the statednumber of pulses calculated from the combined 532-nm damagedata on BK-7 for focal spot radii of 12.5, 14.0, and 14.5 jm. Thecrosses and error bars represent the multiple pulse damage probabil-ities predicted from the single pulse damage data using Eq. (1) with

M= 1.

V. Statistical Test for the Influence of PredamageIrradiation

It has recently been suggested that multiple pulsesurface damage in silicon does not involve predamagematerial changes at all.8 Rather, it is found in thatstudy that the probability of damage after a number ofpulses can be predicted from the single pulse damageprobability at the same fluence by assuming that eachpulse has the same probability of inducing damage. Inthis section the damage data of Sec. III will be testedagainst the predictions of this model.

In this model the probability of damage at a givenfluence within N pulses, PN, is predicted to be relatedto the probability of damage within M pulses, PM, by8

PN(predicted) = 1 - (1 - M)N. (1)

A thorough test of this prediction would require a verylarge data set so that the damage probability in each ofseveral fluence intervals can be determined accurately.This is difficult in view of the destructive nature ofdamage studies. However, data sets adequate for atleast a limited test can be assembled for fused silicaand BK-7 at 532 nm by combining experiments forclosely similar focal spot radii. Data for BK-7 at apulse repetition frequency of 10 Hz with focal spotradii of 12.5, 14.0, and 14.5 Aim, totaling 140 datapoints, have been combined to give the damage proba-bilities shown in Fig. 9. The crosses indicate the prob-abilities predicted from Eq. (1) using M = 1. That is,the probabilities for damage within three, five, and tenpulses are predicted from the single pulse damageprobability for each fluence range. The error bars onthe predictions reflect the limited knowledge of the

single pulse damage probability. For example, if six often sites irradiated in a given fluence range damagedon the first pulse, it is assumed in calculation of PN thatPi is between 0.55 and 0.65.

Despite the limited data set, it is evident from Fig. 9that damage tends to occur at lower fluences afterexposure to several pulses than predicted from thesingle pulse damage data by Eq. (1). Data obtained bycombining the 532-nm, 10-Hz Corning 7940 data forfocal spot sizes of 12.0 and 14.5 Am exhibit the sametrend.

This indicates that the probability of damage at agiven pulse fluence is not the same for each pulse, butrather increases as the sample is exposed to morepulses. Note that this result also argues against thesuggestion7 that multiple pulse damage occurs merelydue to exposure of the sample to an anomalously highirradiance pulse which happens to exceed the singlepulse damage threshold. This is the case becauseoscilloscope observations of the pulse waveform indi-cate that fluctuations of the waveform occur randomly,such that the probability of anomalously high irradi-ance should be the same for each pulse. Rather, thepulses to which a site is exposed prior to observabledamage must modify the sample in such a way as tomake subsequent damage more likely. This confirmsthe conclusion reached for Corning 7940 on the basis ofthe pulse repetition dependence data and extends thatconclusion to include BK-7.

VI. Discussion

It is evident from the pulse repetition frequencydata and the statistical argument that the multiplepulse damage observed in the present study does in-volve the promotion of subsequent damage by laserpulses at fluences below the single pulse threshold.The mechanism for this phenomenon remains unclear,but the data may be used to address some possibilities.

Since there is some variability in damage thresholdand morphology from site to site it is possible thatinclusions, point defects, or other imperfections play arole in the damage process. Further, the growth ofmacroscopic absorption centers such as inclusionsseems to explain multiple pulse damage in some sys-tems.6'28 However, the fact that the damage sites inthe present study appear to follow the high irradianceregion of the beam rather closely suggests that anysuch defects must exist in rather high concentrationand yet must have small enough absorbance for thesample to remain transparent. Together with the lackof growth in absorption or light scattering reported inother damage studies on SiO2,4,5 this makes it unlikelythat absorbing inclusions are important to multiplepulse damage in these materials.

Electron avalanche and multiphoton absorption,the two most widely accepted mechanisms for singlepulse damage in the absence of inclusion heating, havenot been extended to the multiple pulse regime in adetailed way. In either of these mechanisms damageis generally regarded to require the production of somethreshold concentration of conduction band electrons,


resulting in strong absorption and heating. (A plausi-ble concentration criterion is that the plasma frequen-cy becomes comparable with the laser frequency, re-quiring concentrations of the order of from 1020 to 1021cm 3 for visible light.) Since the rate of production ofconduction band electrons in either of these mecha-nisms varies strongly with irradiance, their operationat irradiances below the single pulse damage thresholdwould presumably require an increase in the density ofinitial states from which electrons may be promoted tothe conduction band. In such a scenario the need formany pulses to achieve laser damage at pulse energiesbelow the single pulse threshold would reflect the timerequired to produce sufficient initial states to permitdamage.

The production of such initial states, as, for exam-ple, by the optical generation of point defects, would beconsistent with some aspects of the multiple pulsedamage data. In particular, since some types of pointdefect are transient the pulse repetition frequency de-pendence of the many-pulse damage behavior in fusedsilica would be understandable. However, the insensi-tivity of damage thresholds to the presence of pointdefects introduced by x irradiation in BK-7 or by OHimpurities in fused silica suggests that these particulardefect states are of little importance for multiple pulsedamage.

The null result of the luminescence experimentspresents a further constraint. The simplest model bywhich one may envision the production of states whichcan serve to increase the rate of free-electron genera-tion is one in which the laser light itself generates thestates. In such a case, however, one would expect theconcentration of initial states, and thus the concentra-tion of conduction band electrons produced by eithermultiphoton absorption or electron avalanche, to in-crease linearly from pulse to pulse. Since the detec-tion limit of the luminescence experiment for quartz isseveral orders of magnitude lower than the electronconcentration required for the plasma frequency toapproach the laser frequency, the lack of observableluminescence rules out such a linear growth of concen-tration to damaging levels.

However, it may be premature to rule out the exten-sion of the multiphoton absorption and electron ava-lanche damage mechanisms to the multiple pulse dam-age regime. It is interesting to note that investigatorsof amorphous SiO2 in semiconductor devices have re-ported the generation of long-lived electron traps inthe SiO2 by charge injection.2 9 The rate of trap gener-ation was proportional to the injected charge flux andincreased strongly as the injected electrons were givenmore energy. In addition, it has been found that bom-bardment of SiO 2 by electrons at energies too low todisplace atoms by momentum transfer creates long-lived electron traps.30 These results raise the possibil-ity that, under laser irradiation, states capable of trap-ping electrons for excitation on subsequent pulses maybe created by the conduction band electrons them-selves rather than by the light. In such a case both thenumber of electrons available to be trapped and the

probability of a given electron becoming trapped isproportional to the concentration of conduction bandelectrons, so that the growth of this concentration canvary more strongly than linearly with pulse number.Indeed, in view of the exponential growth of the con-duction band electron concentration during each laserpulse predicted in the electron avalanche model,'5 thegrowth of the concentration may be a sufficientlystrong function of pulse number to be reconciled withthe lack of observable luminescence during multiplepulse irradiation.

Evidently, the data presented here constrain thecharacteristics of any plausible model of multiplepulse damage in SiO 2 but cannot identify the correctmodel. Existing evidence that damage-promotingproperty changes do occur during irradiation is supple-mented by the statistical and pulse repetition frequen-cy data, and yet the point defect and luminescencestudies tend to limit the mechanisms by which damagemay be promoted. However, the primary difficulty ofidentifying the damage mechanism remains, namely,the lack of direct evidence of changing material prop-erties on the pulses preceding catastrophic damage. Itmay be hoped that more sensitive measurements ofoptical properties will improve this situation. Anoth-er interesting possibility would be the performance ofelectron spin resonance measurements during a multi-ple pulse damage experiment. Until direct observa-tions of precatastrophic damage changes are achieved,discussions of the multiple pulse damage mechanismmay have difficulty moving beyond the speculativestage.

The authors wish to thank Alton Armington of theRome Air Development Center, Nicholas Koumvaka-lis of Litton Guidance and Control Systems, and RalphPerkins of the Corning Glass Works for donating sam-ples. They also gratefully acknowledge the financialsupport of the Research Corporation.

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